Wave propagation in magneto-electro-thermo-elastic nanobeams based on nonlocal theory
- PDF / 1,040,370 Bytes
- 15 Pages / 595.276 x 790.866 pts Page_size
- 19 Downloads / 189 Views
(2020) 42:601
TECHNICAL PAPER
Wave propagation in magneto‑electro‑thermo‑elastic nanobeams based on nonlocal theory Dongze He1 · Dongyan Shi1 · Qingshan Wang2 · Chunlong Ma1,3 Received: 22 July 2020 / Accepted: 10 October 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract In this article, wave based method (WBM) is proposed as a new semi-analytical method to analyze the wave propagation characteristics of the magneto-electro-thermo-elastic nanobeams with arbitrary boundary conditions. According to the Timoshenko beam theory and Hamilton principle, the governing equations of the nanobeam which are related to Eringen’s nonlocal theory are obtained. The displacement and external potential variables are expanded as wave function forms. In the light of the introduction of several type boundary conditions, the total matrix of the nanobeam is constituted. Searching the zero locations of the total matrix determinant by the bisection method, the natural frequencies of the nanobeam under arbitrary boundary conditions are received. To further illustrate the calculation correctness of the presented method, the results are compared with the solutions in reported references. Furthermore, a series of numerical examples are proposed to investigate the effect of each parameter on the free vibration characteristics of the nanobeam with several boundary conditions, such as beam length and thickness, external temperature rise, magnetic and electric potential. Some new numerical solutions and conclusions are presented in this paper to provide the basic foundation for subsequent research. Keywords Magneto-electro-thermo-elastic nanobeam · Wave propagation · Wave based method · Nonlocal theory List of symbols σij Stress compositions εij Strain compositions Di Electric displacement Ei Electric field Hi Magnetic field cijkl Elastic constant emij Piezoelectric constants sim Dielectric constants qij Piezomagnetic constants dij Magnetoelectric constants Technical Editor: Samuel da Silva. * Qingshan Wang [email protected] 1
College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, People’s Republic of China
2
State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, People’s Republic of China
3
Department of Automotive Engineering, Harbin Vocational & Technical College, Harbin 150001, People’s Republic of China
μij Magnetic constants pi Pyroelectric constants λi Pyromagnetic constants Ks Shear correction factor θ(x, t) Cross section rotation w(x,t) Transverse displacement Φ(x,t) The change of electric potential Ψ(x,t) The change of magnetic potential ϕ0 Initial external of electric potential Ψ0 Initial external of electric potential ∆T Temperature change e0a(μ) Scale coefficient ∼ Φ (x, z, t) External electric potential variable ∼ Ψ (x, z, t) External magnetic potential variable Mx Bending moment Qx Transverse shear force Ψ0 External magnetic potential ϕ0 External electric po
Data Loading...
